I am a NOLA area resident. The easiest to accomplish local rides are on the MUPs atop the river levee and those that run along Lake Pontchartrain. There is no vehicular traffic on the routes. Google satellite maps show the paths well.
Camping?
https://louisianastateparks.reservea...&parkId=240011
And the Tammany Trace Bike Trail runs right through the park!
I can also recommend riding Highway 51, adjacent to I-55 through the marsh from Laplace LA out and back. There's almost no vehicular traffic, the road has a wide shoulder, and the scenery is kinda cool, especially for someone from out of the area.